Finite Group Databasebeta

← C3×#91256 #13086406

Subgroups — C3×#91256 #13086406

Order 1440.

326 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#6777C212yesmaximal, complemented
2C3×C8×D15C211yesmaximal, characteristic, complemented
3C3×C5×D24C211yesmaximal, characteristic, complemented
4C32×D40C211yesmaximal, characteristic, complemented
5C3×#6652C212yesmaximal, complemented
6C3×D5×D8—31nomaximal
7#91256C311yesmaximal, characteristic, direct product factor
8C2×C3×D3×D5—22no—
9C3×C4×D15C2211yescharacteristic
10C3×C5×D12C2212yescomplemented
11C32×D20C2212yescomplemented
12C3×#1201—22no—
13C32×C5×C8C2211yescharacteristic, complemented
14C3×C3⋊#168C2211yescharacteristic, complemented
15C3×D3×D8—51nomaximal, Hall
16C3×D4×D5—32no—
17#6777C2×C312yescomplemented
18C3×C5×D8—31no—
19C8×D15C2×C311yescharacteristic, complemented
20C5×D24C2×C311yescharacteristic, complemented
21C3×#686—32no—
22C3×D40—21no—
23C3×D40D311yescharacteristic, complemented
24C3×D40C2×C311yescharacteristic, complemented
25C3×C8×D5—31no—
26#6652C2×C312yescomplemented
27C2×C3×D15D411yescharacteristic
28C2×C3×C5×D3—22no—
29C2×C32×D5—22no—
30C3×D3×D5—44no—
31C32×C4×C5C2311yescharacteristic
32C3×Dic15D411yescharacteristic
33D5×D8—31noHall
34C3×D3×D4—52no—
35C32×D8—51no—
36C3×#213—52no—
37C3×D24D511yescharacteristic, complemented
38C3×D3×C8—51no—
39C22×C3×D5—62no—
40C2×D3×D5—22no—
41C3×C5×D4—32no—
42C4×D15C22×C311yescharacteristic
43C5×D12C22×C312yescomplemented
44C3×C22⋊D5—62no—
45C3×D20—22no—
46C3×D20C2×D312yescomplemented
47C3×D20C22×C312yescomplemented
48C3×C4×D5—31no—
49#1201—22no—
50C3×C5×C8—21no—
51C3×C5×C8C2×D311yescharacteristic, complemented
52C3×C5×C8C22×C311yescharacteristic, complemented
53C3⋊#168C22×C311yescharacteristic, complemented
54C3×#168—31no—
55C2×C3×D8—151no—
56D3×D8—51no—
57C2×C32×C5C2×D411yescharacteristic
58C3×D15D812yescomplemented
59C3×C5×D3—42no—
60C32×D5—42no—
61D4×D5—32no—
62C5×D8—31no—
63#686—32no—
64D40C3×D311yescharacteristic, complemented
65C8×D5—31no—
66C22×C3×D3—102no—
67C32×D4—52no—
68C3×#67—102no—
69C3×D12C2×D512yescomplemented
70C3×C4×D3—51no—
71C32×C8C2×D511yescharacteristic, complemented
72C3×C3⋊C8—51no—
73C22×C3×C5—62no—
74C2×D15C3×D411yescharacteristic
75C2×C5×D3—22no—
76C2×C3×D5—22no—
77C2×C3×D5—22no—
78C2×C3×D5—31no—
79C2×C3×D5—42no—
80C2×C3×D5—124no—
81D3×D5—44no—
82C3×C4×C5—21no—
83C3×C4×C5C22×D311yescharacteristic
84C3×C4×C5C23×C311yescharacteristic
85Dic15C3×D411yescharacteristic
86C3×Dic5—31no—
87C2×C3×D4—152no—
88D3×D4—52no—
89C3×D8—31no—
90C3×D8—51no—
91C3×D8—51no—
92C3×D8—101no—
93C3×D8—152no—
94C2×C3×C8—151no—
95#213—52no—
96D24C3×D511yescharacteristic, complemented
97D3×C8—51no—
98C32×C5C2×D811yescharacteristic, complemented, Hall
99C22×D5—62no—
100C5×D4—32no—
101C22⋊D5—62no—
102D20C2×C3×D312yescomplemented
103C4×D5—31no—
104C5×C8C2×C3×D311yescharacteristic, complemented
105#168—31no—
106C22×C32—102no—
107C2×C3×D3—22no—
108C2×C3×D3—51no—
109C2×C3×D3—204no—
110C32×C4C22×D511yescharacteristic
111C3×Dic3—51no—
112C2×D8—151noSylow
113C2×C3×C5—21no—
114C2×C3×C5—122no—
115C2×C3×C5D3×D411yescharacteristic
116C2×C3×C5C2×C3×D411yescharacteristic
117D15C3×D812yescomplemented
118C3×D5—32no—
119C3×D5—42no—
120C3×D5—42no—
121C3×D5—82no—
122C5×D3—42no—
123C23×C3—302no—
124C22×D3—102no—
125C3×D4—32no—
126C3×D4—52no—
127C3×D4—52no—
128C3×D4—102no—
129C3×D4—302no—
130C2×C3×C4—151no—
131#67—102no—
132D12C2×C3×D512yescomplemented
133C4×D3—51no—
134C3×C8—21no—
135C3×C8—151no—
136C3×C8D3×D511yescharacteristic, complemented
137C3×C8C2×C3×D511yescharacteristic, complemented
138C3⋊C8—51no—
139C22×C5—62no—
140C2×D5—22no—
141C2×D5—31no—
142C2×D5—124no—
143C4×C5C22×C3×D311yescharacteristic
144Dic5—31no—
145C2×C32—202no—
146C2×C32D4×D511yescharacteristic
147C3×D3—42no—
148C3×D3—52no—
149C2×D4—152no—
150D8—31no—
151D8—51no—
152D8—152no—
153C2×C8—151no—
154C3×C5—21no—
155C3×C5D3×D811yescharacteristic, complemented
156C3×C5C2×C3×D811yescharacteristic, complemented
157C22×C3—62no—
158C22×C3—102no—
159C22×C3—102no—
160C22×C3—151no—
161C22×C3—202no—
162C22×C3—604no—
163C2×D3—22no—
164C2×D3—51no—
165C2×D3—204no—
166C3×C4—21no—
167C3×C4—151no—
168C3×C4C2×D3×D511yescharacteristic
169C3×C4C22×C3×D511yescharacteristic
170Dic3—51no—
171C2×C5—122no—
172C2×C5C3×D3×D411yescharacteristic
173D5—32no—
174D5—42no—
175C32D5×D811yescharacteristic, complemented, Sylow
176C23—302no—
177D4—32no—
178D4—52no—
179D4—302no—
180C2×C4—151no—
181C8—151no—
182C8C3×D3×D511yescharacteristic, complemented
183C2×C3—21no—
184C2×C3—122no—
185C2×C3—152no—
186C2×C3—202no—
187C2×C3—202no—
188C2×C3—402no—
189C2×C3#677711yescharacteristic
190C2×C3C3×D4×D511yescharacteristic
191D3—42no—
192D3—52no—
193C5C3×D3×D811yescharacteristic, complemented, Sylow
194C22—62no—
195C22—102no—
196C22—151no—
197C22—604no—
198C4—151no—
199C4C2×C3×D3×D511yescharacteristic
200C3—21no—
201C3#9125611yescharacteristic, direct product factor
202C3C3×D5×D811yescharacteristic, complemented
203C2—122no—
204C2—152no—
205C2—202no—
206C2C3×#677711yescharacteristic
subgroupG/H
centerC2×C3#6777
commutator, cosocleC3×C4×C5C23×C3
FrattiniC4C2×C3×D3×D5
FittingC32×C5×C8C22
socleC2×C32×C5C2×D4
hypercenterC3×C8D3×D5
hypocenterC3×C5C2×C3×D8
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#6777C2semidirect
2. C3×C8×D15C2semidirect
3. C3×C5×D24C2semidirect
4. C32×D40C2semidirect
5. C3×#6652C2semidirect
7. #91256C3direct (N × H)
10. C3×C5×D12C22semidirect
11. C32×D20C22semidirect
13. C32×C5×C8C22semidirect
14. C3×C3⋊#168C22semidirect
17. #6777C2×C3semidirect
19. C8×D15C2×C3semidirect
20. C5×D24C2×C3semidirect
23. C3×D40D3semidirect
24. C3×D40C2×C3semidirect
26. #6652C2×C3semidirect
37. C3×D24D5semidirect
43. C5×D12C22×C3semidirect
46. C3×D20C2×D3semidirect
47. C3×D20C22×C3semidirect
51. C3×C5×C8C2×D3semidirect
52. C3×C5×C8C22×C3semidirect
53. C3⋊#168C22×C3semidirect
58. C3×D15D8semidirect
64. D40C3×D3semidirect
69. C3×D12C2×D5semidirect
71. C32×C8C2×D5semidirect
96. D24C3×D5semidirect
98. C32×C5C2×D8semidirect
102. D20C2×C3×D3semidirect
104. C5×C8C2×C3×D3semidirect
117. D15C3×D8semidirect
132. D12C2×C3×D5semidirect
136. C3×C8D3×D5semidirect
137. C3×C8C2×C3×D5semidirect
155. C3×C5D3×D8semidirect
156. C3×C5C2×C3×D8semidirect
175. C32D5×D8semidirect
182. C8C3×D3×D5semidirect
193. C5C3×D3×D8semidirect
201. C3#91256direct (N × H)
202. C3C3×D5×D8semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#67772
C3×C8×D152
C3×C5×D242
C32×D402
C3×#66522
C3×D5×D83
#912563
C3×D3×D85